Subgroups — C₉×D₁₃×D₂₃ #24924486

Order 10764.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₂₉₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×C₂₃×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₁₃×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₃×D₂₃	C₃	1	1	yes	maximal, characteristic
5	C₉×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₂₉₉	C₂×C₃	1	1	yes	characteristic
7	C₃×C₂₃×D₁₃	C₂×C₃	1	1	yes	characteristic
8	C₃×C₁₃×D₂₃	C₂×C₃	1	1	yes	characteristic
9	D₁₃×D₂₃	C₉	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₁₃×C₂₃	C₂²×C₃	1	1	yes	characteristic
11	C₂×C₉×D₂₃	—	13	1	no	maximal, Hall
12	D₂₉₉	C₂×C₉	1	1	yes	characteristic, complemented
13	C₁₃×D₂₃	C₂×C₉	1	1	yes	characteristic, complemented
14	C₂₃×D₁₃	C₂×C₉	1	1	yes	characteristic, complemented
15	C₂×C₉×D₁₃	—	23	1	no	maximal, Hall
16	C₂×C₉×C₂₃	—	13	1	no	—
17	C₉×D₂₃	—	13	1	no	—
18	C₉×D₂₃	D₁₃	1	1	yes	characteristic, direct product factor
19	C₁₃×C₂₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×D₂₃	—	13	1	no	—
21	C₂×C₉×C₁₃	—	23	1	no	—
22	C₉×D₁₃	—	23	1	no	—
23	C₉×D₁₃	D₂₃	1	1	yes	characteristic, direct product factor
24	C₉×C₂₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×D₁₃	—	23	1	no	—
26	C₂×C₃×C₂₃	—	13	1	no	—
27	C₃×D₂₃	—	13	1	no	—
28	C₃×D₂₃	C₃×D₁₃	1	1	yes	characteristic
29	C₉×C₁₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
30	C₂×D₂₃	—	13	1	no	Hall
31	C₂×C₃×C₁₃	—	23	1	no	—
32	C₃×D₁₃	—	23	1	no	—
33	C₃×D₁₃	C₃×D₂₃	1	1	yes	characteristic
34	C₃×C₂₃	C₂×C₃×D₁₃	1	1	yes	characteristic
35	C₂×D₁₃	—	23	1	no	Hall
36	C₂×C₂₃	—	13	1	no	—
37	D₂₃	—	13	1	no	—
38	D₂₃	C₉×D₁₃	1	1	yes	characteristic, direct product factor
39	C₃×C₁₃	C₂×C₃×D₂₃	1	1	yes	characteristic
40	C₂²×C₉	—	299	1	no	Hall
41	C₂×C₁₃	—	23	1	no	—
42	D₁₃	—	23	1	no	—
43	D₁₃	C₉×D₂₃	1	1	yes	characteristic, direct product factor
44	C₂₃	C₂×C₉×D₁₃	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₉	—	13	1	no	—
46	C₂×C₉	—	23	1	no	—
47	C₂×C₉	—	299	1	no	—
48	C₁₃	C₂×C₉×D₂₃	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₃	—	299	1	no	—
50	C₉	D₁₃×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₃	—	13	1	no	—
52	C₂×C₃	—	23	1	no	—
53	C₂×C₃	—	299	1	no	—
54	C₂²	—	299	1	no	Sylow
55	C₃	C₃×D₁₃×D₂₃	1	1	yes	characteristic
56	C₂	—	13	1	no	—
57	C₂	—	23	1	no	—
58	C₂	—	299	1	no	—

	subgroup	G/H
center, hypercenter	C₉	D₁₃×D₂₃
commutator, hypocenter	C₁₃×C₂₃	C₂²×C₉
Frattini	C₃	C₃×D₁₃×D₂₃
Fitting	C₉×C₁₃×C₂₃	C₂²
socle, cosocle	C₃×C₁₃×C₂₃	C₂²×C₃
prime radical	C₃×D₁₃×D₂₃	C₃
LCS	G ▷ C₁₃×C₂₃
UCS	C₁ ◁ C₉

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₉×D₂₉₉	C₂	semidirect
2. C₉×C₂₃×D₁₃	C₂	semidirect
3. C₉×C₁₃×D₂₃	C₂	semidirect
5. C₉×C₁₃×C₂₃	C₂²	semidirect
9. D₁₃×D₂₃	C₉	direct (N × H)
12. D₂₉₉	C₂×C₉	semidirect
13. C₁₃×D₂₃	C₂×C₉	semidirect
14. C₂₃×D₁₃	C₂×C₉	semidirect
18. C₉×D₂₃	D₁₃	direct (N × H)
19. C₁₃×C₂₃	C₂²×C₉	semidirect
23. C₉×D₁₃	D₂₃	direct (N × H)
24. C₉×C₂₃	C₂×D₁₃	semidirect
29. C₉×C₁₃	C₂×D₂₃	semidirect
38. D₂₃	C₉×D₁₃	direct (N × H)
43. D₁₃	C₉×D₂₃	direct (N × H)
44. C₂₃	C₂×C₉×D₁₃	semidirect
48. C₁₃	C₂×C₉×D₂₃	semidirect
50. C₉	D₁₃×D₂₃	direct (N × H)

Subgroups — C9×D13×D23 #24924486

Conjugacy classes of subgroups

Complements

Subgroups — C₉×D₁₃×D₂₃ #24924486